| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 396.2-c3 |
396.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
396.2 |
\( 2^{2} \cdot 3^{2} \cdot 11 \) |
\( 2^{4} \cdot 3^{6} \cdot 11^{2} \) |
$1.32208$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$3.738805730$ |
2.254584685 |
\( \frac{18609625}{1188} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -6\) , \( 4\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-6{x}+4$ |
| 3564.3-c3 |
3564.3-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3564.3 |
\( 2^{2} \cdot 3^{4} \cdot 11 \) |
\( 2^{4} \cdot 3^{18} \cdot 11^{2} \) |
$2.28991$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{4} \) |
$0.673324078$ |
$1.246268576$ |
4.048176412 |
\( \frac{18609625}{1188} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -50\) , \( -115\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-50{x}-115$ |
| 9900.4-f3 |
9900.4-f |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9900.4 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 11^{2} \) |
$2.95627$ |
$(-a), (a-1), (-a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.338959345$ |
$1.672044753$ |
4.101194898 |
\( \frac{18609625}{1188} \) |
\( \bigl[a\) , \( 1\) , \( 1\) , \( -17 a + 11\) , \( 17 a - 47\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-17a+11\right){x}+17a-47$ |
| 9900.6-d3 |
9900.6-d |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9900.6 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
\( 2^{4} \cdot 3^{6} \cdot 5^{6} \cdot 11^{2} \) |
$2.95627$ |
$(-a), (a-1), (a-2), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.338959345$ |
$1.672044753$ |
4.101194898 |
\( \frac{18609625}{1188} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 16 a - 6\) , \( -17 a - 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(16a-6\right){x}-17a-30$ |
| 13068.2-c3 |
13068.2-c |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13068.2 |
\( 2^{2} \cdot 3^{3} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 11^{8} \) |
$3.16874$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.650842537$ |
1.569891268 |
\( \frac{18609625}{1188} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 60 a - 180\) , \( -435 a + 884\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(60a-180\right){x}-435a+884$ |
| 13068.3-e3 |
13068.3-e |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
13068.3 |
\( 2^{2} \cdot 3^{3} \cdot 11^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 11^{8} \) |
$3.16874$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.650842537$ |
1.569891268 |
\( \frac{18609625}{1188} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -62 a - 119\) , \( 434 a + 449\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-62a-119\right){x}+434a+449$ |
| 25344.2-f3 |
25344.2-f |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25344.2 |
\( 2^{8} \cdot 3^{2} \cdot 11 \) |
\( 2^{28} \cdot 3^{6} \cdot 11^{2} \) |
$3.73942$ |
$(-a), (a-1), (-2a+1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$1.418470229$ |
$0.934701432$ |
6.396122512 |
\( \frac{18609625}{1188} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -88\) , \( -272\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-88{x}-272$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
